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   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 1.6: Moving average\n",
    "\n",
    "### 1.6.1: Time Series moving average\n",
    "\n",
    "When reviewing how a time series changes (i.e. $\\Delta X_t$), the error itself is normally random (called *white noise*) over time, but may have some dependency on the previous value.\n",
    "\n",
    "For instance, if a stock increases in price one day, this may lead investors to sell their stock, leading to a decreasing (or a return to the mean) on the second day.\n",
    "\n",
    "If we denote a positive $\\epsilon_t$ to be an increase in buying for a given stock at time period $t$, we can model a stock's price change simply using the equation:\n",
    "\n",
    "$\\Delta p_t = \\epsilon_t - 0.5 \\epsilon_{t-1}$\n",
    "\n",
    "That is, the price increases if there is more buying today, with a negative factor if there was more buying yesterday. This type of model is known as a moving average process, specifically one of order 1 (because we are only modelling one time step in the past). We denote this model a $MA(n)$ process for time steps of $n$, and the one above is a $MA(1)$ process because it cares about one step in the past.\n",
    "\n",
    "Note: The process is an MA(1) process whether the coefficient on $\\epsilon_{t-1}$ is positive or negative.\n",
    "\n",
    "More formally, a MA(n) process is:\n",
    "\n",
    "$MA(p) X_t = \\mu + \\epsilon_{t} + \\sum_{i=1}^{p}\\theta_i\\epsilon_{t-i}$\n",
    "\n",
    "Where $\\mu$ is the error term (assumed to be iid) and $\\theta_i$ is a learned parameter in the model (learned, say, from an OLS). The equation for MA(1) is the same, but it is worth noting it, as you'll see the pattern in quite a few places. We'll drop $\\mu$ from the equation, and set $p=1$, giving:\n",
    "\n",
    "$MA(1)X_t = \\epsilon_t + \\theta \\epsilon_{t-1}$\n",
    "\n",
    "Notably, and importantly, $\\epsilon$ is assumed to be independently and identically distributed from a normal distribution with a mean of 0 and a standard deviation (of $\\sigma^2$). This is an important requirement, otherwise the model has other patterns in it that need to be modelled separately.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    In the above equation, we used $\\theta$ as the parameter, while our previous models used $\\beta$. It doesn't matter; they are the same thing. The choice here is for two reasons. First, most textbooks use $\\theta$ in this spot. Second, we will combine an MA model with another model later, so we need the different symbols then.\n",
    "</div>\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    Further, in the example, we modeled the change in some variable. This is not a requirement, as the values $X$ can be any variable, including (but not limited to) the change in value of some process.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run setup.ipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate some random data for our epsilons, remembering they are iid\n",
    "\n",
    "epsilons = np.random.randn(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.array([-0.5])\n",
    "\n",
    "X_t = epsilons[1:] + theta * epsilons[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13ed9185b50>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fit a MA model. statsmodels doesn't expose this nicely directly, so we use ARMA, and turn \"off\" the AR bit.\n",
    "# We will look at the full ARMA model later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels as sm\n",
    "model = sm.tsa.arima.model.ARIMA(X_t, order=(0,0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>SARIMAX Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>    <td>999</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARIMA(0, 0, 1)</td>  <th>  Log Likelihood     </th> <td>-1416.541</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Wed, 07 Feb 2024</td> <th>  AIC                </th> <td>2839.082</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>00:57:30</td>     <th>  BIC                </th> <td>2853.803</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>                  <td>0</td>        <th>  HQIC               </th> <td>2844.677</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                      <td> - 999</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>opg</td>       <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.0102</td> <td>    0.016</td> <td>    0.654</td> <td> 0.513</td> <td>   -0.020</td> <td>    0.041</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1</th>  <td>   -0.5086</td> <td>    0.026</td> <td>  -19.819</td> <td> 0.000</td> <td>   -0.559</td> <td>   -0.458</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.9977</td> <td>    0.041</td> <td>   24.210</td> <td> 0.000</td> <td>    0.917</td> <td>    1.079</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Ljung-Box (L1) (Q):</th>     <td>0.64</td> <th>  Jarque-Bera (JB):  </th> <td>8.75</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Q):</th>                <td>0.42</td> <th>  Prob(JB):          </th> <td>0.01</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Heteroskedasticity (H):</th> <td>1.20</td> <th>  Skew:              </th> <td>0.14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(H) (two-sided):</th>    <td>0.10</td> <th>  Kurtosis:          </th> <td>3.37</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                               SARIMAX Results                                \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  999\n",
       "Model:                 ARIMA(0, 0, 1)   Log Likelihood               -1416.541\n",
       "Date:                Wed, 07 Feb 2024   AIC                           2839.082\n",
       "Time:                        00:57:30   BIC                           2853.803\n",
       "Sample:                             0   HQIC                          2844.677\n",
       "                                - 999                                         \n",
       "Covariance Type:                  opg                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0102      0.016      0.654      0.513      -0.020       0.041\n",
       "ma.L1         -0.5086      0.026    -19.819      0.000      -0.559      -0.458\n",
       "sigma2         0.9977      0.041     24.210      0.000       0.917       1.079\n",
       "===================================================================================\n",
       "Ljung-Box (L1) (Q):                   0.64   Jarque-Bera (JB):                 8.75\n",
       "Prob(Q):                              0.42   Prob(JB):                         0.01\n",
       "Heteroskedasticity (H):               1.20   Skew:                             0.14\n",
       "Prob(H) (two-sided):                  0.10   Kurtosis:                         3.37\n",
       "===================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
       "\"\"\""
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the coefficient for `ma.L1.y` is approximately our theta value from where we created this data - the model fit it well. The constant coefficient is zero too, which indicates it \"learned\" the zero mean correctly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import quandl\n",
    "\n",
    "interest_rates = quandl.get(\"RBA/F13_FOOIRATCR\")\n",
    "interest_rates = interest_rates[interest_rates.columns[0]]  # Extract the first column, whatever it is called\n",
    "interest_rates.name = \"InterestRate\"  # Rename, as the original had a long name. Hint: don't use spaces or special chars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "1990-01-31    17.0\n",
       "1990-02-28    16.5\n",
       "1990-03-31    16.5\n",
       "1990-04-30    15.0\n",
       "1990-05-31    15.0\n",
       "              ... \n",
       "2021-02-28     0.1\n",
       "2021-03-31     0.1\n",
       "2021-04-30     0.1\n",
       "2021-05-31     0.1\n",
       "2021-06-30     0.1\n",
       "Name: InterestRate, Length: 378, dtype: float64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interest_rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency M will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    }
   ],
   "source": [
    "model = sm.tsa.ARMA(interest_rates, order=(0, 1))\n",
    "interest_results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>InterestRate</td>   <th>  No. Observations:  </th>    <td>378</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(0, 1)</td>    <th>  Log Likelihood     </th> <td>-709.234</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.576</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 17 Feb 2022</td> <th>  AIC                </th> <td>1424.468</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>19:25:18</td>     <th>  BIC                </th> <td>1436.273</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-31-1990</td>    <th>  HQIC               </th> <td>1429.153</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 06-30-2021</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>              <td>    4.8175</td> <td>    0.155</td> <td>   31.031</td> <td> 0.000</td> <td>    4.513</td> <td>    5.122</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.InterestRate</th> <td>    0.9176</td> <td>    0.014</td> <td>   63.839</td> <td> 0.000</td> <td>    0.889</td> <td>    0.946</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -1.0898</td> <td>          +0.0000j</td> <td>           1.0898</td> <td>           0.5000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:           InterestRate   No. Observations:                  378\n",
       "Model:                     ARMA(0, 1)   Log Likelihood                -709.234\n",
       "Method:                       css-mle   S.D. of innovations              1.576\n",
       "Date:                Thu, 17 Feb 2022   AIC                           1424.468\n",
       "Time:                        19:25:18   BIC                           1436.273\n",
       "Sample:                    01-31-1990   HQIC                          1429.153\n",
       "                         - 06-30-2021                                         \n",
       "======================================================================================\n",
       "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "const                  4.8175      0.155     31.031      0.000       4.513       5.122\n",
       "ma.L1.InterestRate     0.9176      0.014     63.839      0.000       0.889       0.946\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "MA.1           -1.0898           +0.0000j            1.0898            0.5000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interest_results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercises\n",
    "\n",
    "1. Fit an MA model to a stock price (the solution uses AAPL).\n",
    "2. What are the coefficients on the constant and lag? What does this mean?\n",
    "3. Fit the model on the change in stock price, rather than the actual price.\n",
    "4. What are the coefficients, and how does that relate to the change in price?\n",
    "\n",
    "\n",
    "#### Extended Exercise\n",
    "\n",
    "We are going to drill right down now into a small dataset and observe how a $\\epsilon$ value changes the result of the MA(1) model. Create a small dataset of just ten $\\epsilon$ values of random 0s and 1s. Visualise the resulting MA model with a theta value of 0.5, -0.5, 2, -2, 100 and -100. Observe how runs of 0s and 1s are affected, and how a value affects the next time period in the series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import my_secrets\n",
    "quandl.ApiConfig.api_key = my_secrets.QUANDL_API_KEY\n",
    "\n",
    "data = quandl.get_table('WIKI/PRICES', ticker = ['AAPL'], \n",
    "                        qopts = { 'columns': ['adj_close'] }, \n",
    "                        date = { 'gte': '2017-01-01', 'lte': '2019-01-01' }, \n",
    "                        paginate=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "adj_close    154.137248\n",
       "dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>     <td>adj_close</td>    <th>  No. Observations:  </th>    <td>308</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(0, 1)</td>    <th>  Log Likelihood     </th> <td>-1105.727</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>8.735</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 17 Feb 2022</td> <th>  AIC                </th> <td>2217.453</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>19:52:56</td>     <th>  BIC                </th> <td>2228.643</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>                <td>0</td>        <th>  HQIC               </th> <td>2221.928</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                       <td> </td>        <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "         <td></td>            <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>           <td>  154.0698</td> <td>    0.968</td> <td>  159.159</td> <td> 0.000</td> <td>  152.173</td> <td>  155.967</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.adj_close</th> <td>    0.9479</td> <td>    0.012</td> <td>   76.023</td> <td> 0.000</td> <td>    0.923</td> <td>    0.972</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>          -1.0549</td> <td>          +0.0000j</td> <td>           1.0549</td> <td>           0.5000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:              adj_close   No. Observations:                  308\n",
       "Model:                     ARMA(0, 1)   Log Likelihood               -1105.727\n",
       "Method:                       css-mle   S.D. of innovations              8.735\n",
       "Date:                Thu, 17 Feb 2022   AIC                           2217.453\n",
       "Time:                        19:52:56   BIC                           2228.643\n",
       "Sample:                             0   HQIC                          2221.928\n",
       "                                                                              \n",
       "===================================================================================\n",
       "                      coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------\n",
       "const             154.0698      0.968    159.159      0.000     152.173     155.967\n",
       "ma.L1.adj_close     0.9479      0.012     76.023      0.000       0.923       0.972\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "MA.1           -1.0549           +0.0000j            1.0549            0.5000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_n2 = data[\"adj_close\"].dropna()\n",
    "data_n2\n",
    "model2 = sm.tsa.ARMA(data_n2, order=(0, 1))\n",
    "results2 = model2.fit()\n",
    "results2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:215: ValueWarning: An unsupported index was provided and will be ignored when e.g. forecasting.\n",
      "  ' ignored when e.g. forecasting.', ValueWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>     <td>adj_close</td>    <th>  No. Observations:  </th>    <td>307</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(0, 1)</td>    <th>  Log Likelihood     </th> <td>-641.062</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.953</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 17 Feb 2022</td> <th>  AIC                </th> <td>1288.124</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>19:34:44</td>     <th>  BIC                </th> <td>1299.305</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>                <td>0</td>        <th>  HQIC               </th> <td>1292.595</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                       <td> </td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "         <td></td>            <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>           <td>   -0.1741</td> <td>    0.115</td> <td>   -1.513</td> <td> 0.131</td> <td>   -0.400</td> <td>    0.051</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.adj_close</th> <td>    0.0327</td> <td>    0.062</td> <td>    0.528</td> <td> 0.598</td> <td>   -0.089</td> <td>    0.154</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th> <td>         -30.5971</td> <td>          +0.0000j</td> <td>          30.5971</td> <td>           0.5000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:              adj_close   No. Observations:                  307\n",
       "Model:                     ARMA(0, 1)   Log Likelihood                -641.062\n",
       "Method:                       css-mle   S.D. of innovations              1.953\n",
       "Date:                Thu, 17 Feb 2022   AIC                           1288.124\n",
       "Time:                        19:34:44   BIC                           1299.305\n",
       "Sample:                             0   HQIC                          1292.595\n",
       "                                                                              \n",
       "===================================================================================\n",
       "                      coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------\n",
       "const              -0.1741      0.115     -1.513      0.131      -0.400       0.051\n",
       "ma.L1.adj_close     0.0327      0.062      0.528      0.598      -0.089       0.154\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                  Real          Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "MA.1          -30.5971           +0.0000j           30.5971            0.5000\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_n = data[\"adj_close\"].diff().dropna()\n",
    "data_n\n",
    "model1 = sm.tsa.ARMA(data_n, order=(0, 1))\n",
    "results1 = model1.fit()\n",
    "results1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. The const coef explains the mean price of 154.0698, and the ma.L1.adj_close indicates the price is increasing by  0.9479 multiplied by the previous days error.\n",
    "4. The mean change in price is negative 17 cents, and the ma.L1.adj_close indicates the price is increasing by  0.0327 multiplied by the previous days error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "epsilons = np.array([1, 0, 0, 1, 0, 1, 1, 0, 1, 0]) # Try different combinations here.\n",
    "theta_list = [0.5, -0.5, 2, -2, 100,-100]\n",
    "\n",
    "for theta in theta_list:\n",
    "    X = epsilons[1:] + theta * epsilons[:-1]\n",
    "    print(np.mean(epsilons))\n",
    "    \n",
    "    lab = \"X (theta = \" + str(theta) + \")\"\n",
    "    plt.plot(X, label=lab)\n",
    "    plt.plot(epsilons, label='epsilons')\n",
    "    plt.legend()\n",
    "    plt.show()    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/ma_model.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties of MA(1)\n",
    "\n",
    "We can identify that the MA(1) process has an expected value of zero. Because the $\\epsilon$ terms are iid with a mean of 0, the expected value for these values is 0. This gives us:\n",
    "\n",
    "$E[X_t] = E[\\epsilon_t + \\theta \\epsilon_{t-1}] = E[\\epsilon_t] + \\theta E[\\epsilon_{t-1}] = 0$\n",
    "\n",
    "Also note that $\\theta$ is constant, and when you have a constant it can be taken out of the $E$. So, for constant $\\theta$:\n",
    "\n",
    "$E[\\theta \\epsilon] = \\theta E[\\epsilon]$\n",
    "\n",
    "Next, we know the variance of $X_t$, again, because the values of $\\epsilon$ are iid, with a mean of 0, and a standard deviation of $\\sigma^2$ (from the definition). This gives us:\n",
    "\n",
    "$Var(X_t) = Var(\\epsilon_{t} + \\theta \\epsilon_{t-1} = Var(\\epsilon_{t}) + \\theta^2 Var(\\epsilon_{t-1})$\n",
    "\n",
    "Plugging in the known $Var(\\epsilon_{t}) = \\sigma^2$ gives us:\n",
    "\n",
    "$Var(X_t) = \\sigma^2 + \\theta^2\\sigma^2 = \\sigma^2(1 + \\theta^2)$\n",
    "\n",
    "Finally, we could intuitively guess that the covariance at lagged intervales would approximate 0 for lags larger than the period of the MA model. More formally, if $i > 1$, then :\n",
    "\n",
    "$Cov(X_t, X_{t-i}) = Cov(\\epsilon_{t} + \\theta\\epsilon_{t-1}, \\epsilon_{t-i} + \\theta\\epsilon_{t-i-i}) = 0$\n",
    "\n",
    "This is because $\\epsilon_{t}$ is iid (sidenote: this is a very useful property in statistics!) and there are no terms overlapping between the two $X$ lags being computed on. However, when $i=1$ there is an overlap, and the covariance is no longer 0:\n",
    "\n",
    "$Cov(X_t, X_{t-1}) = Cov(\\epsilon_{t} + \\theta\\epsilon_{t-1}, \\epsilon_{t-1} + \\theta\\epsilon_{t-2})$\n",
    "\n",
    "Once more, as $\\epsilon_{t}$ is iid, when we expand this covariance, we only need to evaluate $Cov(\\theta\\epsilon_{t-1}, \\epsilon_{t-1})$ as $Cov(\\epsilon_{t}, \\epsilon_{t+h})=0$ whenever $h \\neq 0$.\n",
    "\n",
    "$Cov(X_t, X_{t-1}) = \\theta Cov(\\epsilon_{t-1}, \\epsilon_{t-1}) = \\theta \\sigma^2$\n",
    "\n",
    "As $Cov(X_t, X_t+h)$ only depends on $h$ (i.e. only the lag matters, not when it was), the covariance doesn't change with time.\n",
    "\n",
    "These three properties indicate that the MA(1) process is stationary. A property we will look at further in the next module."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Extended Exercise\n",
    "\n",
    "1. Does an MA(2) model have an expected value of 0?\n",
    "2. Does an MA(2) model have a covariance tending to 0 with increasing time lags?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Yes, would still have mean 0.\n",
    "2. Yes, because i > 1."
   ]
  }
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